If three consecutive ordinates are taken at 2 m intervals from a traverse line and measured as 1.8 m, 2.5 m and 2.0 m , then the area between the traverse line, the first and last ordinates and the boundary, by trapezoidal rule, is

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JKSSB JE (Civil) Official Paper (Held On: 19 Nov, 2023)
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  1. 17.6 sq m
  2. 8.8 sq m
  3. 18.8 sq m
  4. 7.6 sq m

Answer (Detailed Solution Below)

Option 2 : 8.8 sq m
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Detailed Solution

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Explanation:

To find the area between the traverse line and the ordinates using the trapezoidal rule, we can use the formula:

\(A = {{h} \over 2}(y_0+2y_1+y_2)\)

where h is the interval between the ordinates, y0 is the first ordinate, y1 is the middle ordinate, and y2 is the last ordinate.

Calculation:

Given Data: y0 = 1.8 m, y1 = 2.5 m, and y2 = 2.0 m

h = 2.0 m

\(A = {{2} \over 2}(1.8+2\times2.5+2)\)

A = 8.8 sqm

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